How can I easily animate cutaway views on multiple objects?
Modifiers
Solidify and boolean modifiers should work fine.
You can use CtrlL to copy modifiers from the active object to the selected objects:

Add the solidify and boolean modifiers to one object.

Select other objects you want to bisect, keeping the object with the modifiers active (last selected).

Press CtrlL&gt; Modifiers


Rendering
By creating a node group like this:

By changing the bottom value input on the greater than node, you can adjust where the bisection takes place.
By default it will use the local coordinates of the object, but if you want to use global coordinates you can use a vector transform node, however 0,0,0 will still be at the object origin (see bottom example for using global origin):

To control this for multiple materials at once, add the node group to the end of the node tree:

Result:

If you want to use global coordinates with 0,0,0 at the world center, use the Position output of the geometry node instead:

This probably works better with multiple objects.